We investigate the effect of strong electron-electron repulsion on the electron-phonon interaction from a Fermi-liquid point of view. In particular, we show that the strong interaction is responsible for vertex corrections, which are strongly dependent on the ${\mathit{v}}_{\mathit{F}}$ q/\ensuremath{\omega} ratio, where ${\mathit{v}}_{\mathit{F}}$ is the Fermi velocity and q and \ensuremath{\omega} are the transferred momentum and frequency, respectively. These corrections generically lead to a strong suppression of the effective coupling between quasiparticles mediated by a single phonon exchange in the ${\mathit{v}}_{\mathit{F}}$ q/\ensuremath{\omega}\ensuremath{\gg}1 limit. However, such effect is not present when ${\mathit{v}}_{\mathit{F}}$ q/\ensuremath{\omega}\ensuremath{\ll}1. Analyzing the stability criterion for the compressibility, which involves the effective interactions in the dynamical limit, we show that a sizable electron-phonon interaction can push the system towards a phase separation instability. A detailed analysis is then carried out using a slave-boson approach for the infinite-U three-band Hubbard model describing the basic structure of a ${\mathrm{CuO}}_{2}$ plane in copper oxides. In the presence of a coupling between the local hole density and a dispersionless optical phonon, we explicitly confirm the strong dependence of the hole-phonon coupling on the transferred momentum versus frequency ratio. We also find that the exchange of phonons leads to an unstable phase with negative compressibility already at small values of the bare hole-phonon coupling. Close to the unstable region, we detect Cooper instabilities both in s- and d-wave channels supporting a possible connection between phase separation and superconductivity in strongly correlated systems.We investigate the effect of strong electron-electron repulsion on the electron-phonon interaction from a Fermi-liquid point of view. In particular, we show that the strong interaction is responsible for vertex corrections, which are strongly dependent on the ${\mathit{v}}_{\mathit{F}}$q/\ensuremath{\omega} ratio, where ${\mathit{v}}_{\mathit{F}}$ is the Fermi velocity and q and \ensuremath{\omega} are the transferred momentum and frequency, respectively. These corrections generically lead to a strong suppression of the effective coupling between quasiparticles mediated by a single phonon exchange in the ${\mathit{v}}_{\mathit{F}}$q/\ensuremath{\omega}\ensuremath{\gg}1 limit. However, such effect is not present when ${\mathit{v}}_{\mathit{F}}$q/\ensuremath{\omega}\ensuremath{\ll}1. Analyzing the stability criterion for the compressibility, which involves the effective interactions in the dynamical limit, we show that a sizable electron-phonon interaction can push the system towards a phase separation instability. A detailed analysis is then carried out using a slave-boson approach for the infinite-U three-band Hubbard model describing the basic structure of a ${\mathrm{CuO}}_{2}$ plane in copper oxides. In the presence of a coupling between the local hole density and a dispersionless optical phonon, we explicitly confirm the strong dependence of the hole-phonon coupling on the transferred momentum versus frequency ratio. We also find that the exchange of phonons leads to an unstable phase with negative compressibility already at small values of the bare hole-phonon coupling. Close to the unstable region, we detect Cooper instabilities both in s- and d-wave channels supporting a possible connection between phase separation and superconductivity in strongly correlated systems.

arXiv:cond-mat/9404019Physical review. B, Condensed matterDec 15, 1994128 citations

Excitations and superconductivity in the two-dimensional t-J model

Y. Ohta, Tomohiro Shimozato, R. Eder +1 more

Physica C SuperconductivityDec 1, 19940 citations

Coupling to Optical Phonons in the One-Dimensional t - J Model: Effects on the Superconducting Fluctuations and Phase Separation

R. Fehrenbacher

The one-dimensional $t\ensuremath{-}J$ Holstein model is studied by exact diagonalization of finite rings using a variational approximation for the phonon states. Because of renormalization effects induced by the phonons, for intermediate electron-phonon coupling, the phase separation boundary, and with it the region of dominating superconducting fluctuations is shifted substantially to smaller values of $J/t$ as compared to the pure $t\ensuremath{-}J$ model. Superconducting correlations are weakened through charge density wave interactions mediated by the phonons. Possible consequences for the high- ${T}_{c}$ oxides are discussed.The one-dimensional $t\ensuremath{-}J$ Holstein model is studied by exact diagonalization of finite rings using a variational approximation for the phonon states. Because of renormalization effects induced by the phonons, for intermediate electron-phonon coupling, the phase separation boundary, and with it the region of dominating superconducting fluctuations is shifted substantially to smaller values of $J/t$ as compared to the pure $t\ensuremath{-}J$ model. Superconducting correlations are weakened through charge density wave interactions mediated by the phonons. Possible consequences for the high- ${T}_{c}$ oxides are discussed.

arXiv:cond-mat/9605190Physical Review LettersSep 9, 199613 citations

Impurity effect in the superconducting state of the two-dimensional t–J model

Hiroki Tsuchiura, Yukio Tanaka, Masao Ogata +1 more

Physica C SuperconductivityMay 1, 19990 citations

Phonon Mediated Interaction In The Two-Dimensional t-J Model

N. S. Mondal, Nanda Kumar Ghosh, Alka B. Garg +2 more

AIP conference proceedingsJan 1, 20110 citations

{\mathit{v}}_{\mathit{F}}

q/\ensuremath{\omega} ratio, where

{\mathit{v}}_{\mathit{F}}

is the Fermi velocity and q and \ensuremath{\omega} are the transferred momentum and frequency, respectively. These corrections generically lead to a strong suppression of the effective coupling between quasiparticles mediated by a single phonon exchange in the

{\mathit{v}}_{\mathit{F}}

q/\ensuremath{\omega}\ensuremath{\gg}1 limit. However, such effect is not present when

{\mathit{v}}_{\mathit{F}}

q/\ensuremath{\omega}\ensuremath{\ll}1. Analyzing the stability criterion for the compressibility, which involves the effective interactions in the dynamical limit, we show that a sizable electron-phonon interaction can push the system towards a phase separation instability. A detailed analysis is then carried out using a slave-boson approach for the infinite-U three-band Hubbard model describing the basic structure of a

{\mathrm{CuO}}_{2}

plane in copper oxides. In the presence of a coupling between the local hole density and a dispersionless optical phonon, we explicitly confirm the strong dependence of the hole-phonon coupling on the transferred momentum versus frequency ratio. We also find that the exchange of phonons leads to an unstable phase with negative compressibility already at small values of the bare hole-phonon coupling. Close to the unstable region, we detect Cooper instabilities both in s- and d-wave channels supporting a possible connection between phase separation and superconductivity in strongly correlated systems.

J/t

as compared to the pure $t\ensuremath{-}J$ model. Superconducting correlations are weakened through charge density wave interactions mediated by the phonons. Possible consequences for the high-

{T}_{c}

oxides are discussed.